Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 3

Speedup: 1.0×

• 21.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) z))

C

double code(double x, double y, double z) {
	return (x + y) * z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * z
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * z;
}

Python

def code(x, y, z):
	return (x + y) * z

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) z))

C

double code(double x, double y, double z) {
	return (x + y) * z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * z
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * z;
}

Python

def code(x, y, z):
	return (x + y) * z

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(y + x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* z (+ y x)))

C

double code(double x, double y, double z) {
	return z * (y + x);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z * (y + x)
end function

Java

public static double code(double x, double y, double z) {
	return z * (y + x);
}

Python

def code(x, y, z):
	return z * (y + x)

Julia

function code(x, y, z)
	return Float64(z * Float64(y + x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z * (y + x);
end

Wolfram

code[x_, y_, z_] := N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot z \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto z \cdot \left(y + x\right) \]
4. Add Preprocessing

Alternative 2: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(y + x\right) \leq -4 \cdot 10^{-318}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z (+ y x)) -4e-318) (* z x) (* z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * (y + x)) <= -4e-318) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z * (y + x)) <= (-4d-318)) then
        tmp = z * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * (y + x)) <= -4e-318) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * (y + x)) <= -4e-318:
		tmp = z * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * Float64(y + x)) <= -4e-318)
		tmp = Float64(z * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * (y + x)) <= -4e-318)
		tmp = z * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision], -4e-318], N[(z * x), $MachinePrecision], N[(z * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 x y) z) < -3.9999999e-318

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 51.6

         \[\leadsto \color{blue}{x \cdot z} \]

   5. Applied rewrites 51.6%

      \[\leadsto \color{blue}{x \cdot z} \]

   if -3.9999999e-318 < (*.f64 (+.f64 x y) z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot y} \]

      2. lower-*.f64 55.7

         \[\leadsto \color{blue}{z \cdot y} \]

   5. Applied rewrites 55.7%

      \[\leadsto \color{blue}{z \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y + x\right) \leq -4 \cdot 10^{-318}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024230 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))